This report presents the flow and heat transfer characteristics of MHD micropolar fluid due to the stretching of a surface with second order velocity slip. The influence of nonlinear radiation and irregular heat source/sink are anticipated. Simultaneous solutions are presented for first and second-order velocity slips. The PDEs which govern the flow have been transformed as ODEs by the choice of suitable similarity transformations. The transformed nonlinear ODEs are converted into linear by shooting method then solved numerically by fourth-order Runge-Kutta method. Graphs are drowned to discern the effect of varied nondimensional parameters on the flow fields (velocity, microrotation, and temperature). Along with them the coefficients of Skin friction, couple stress, and local Nussel number are also anticipated and portrayed with the support of the table. The results unveil that the non-uniform heat source/sink and non-linear radiation parameters plays a key role in the heat transfer performance. Also, second-order slip velocity causes strengthen in the distribution of velocity but a reduction in the distribution of temperature is perceived.

We introduce the notion of gravity coupled to a horizontally conformal submersion as a modification of the well-known concept of gravity coupled to a harmonic map, thus obtaining a coupled gravity system with a more geometric flavor. By using integral techniques we determine the necessary conditions for coupling and cosmological constants. Finally, in the context of higher dimensional gravitation theory, we show that harmonic morphisms provide a natural ansatz to trigger spontaneous splitting and reduction of the gravity system coupled to a harmonic map on $\text{(4+D)}$ $\text{(D⩾1)}$ dimensional space–times.

We have proposed a robust, secure and efficient image encryption algorithm based on chaotic maps and algebraic structure. Nowadays, the chaotic cryptosystems gained more attention due to their efficiency, the assurance of robustness and high sensitivity corresponding to initial conditions. In literature, there are many encryption algorithms that can simply guarantees security while the schemes based on chaotic systems only promises the uncertainty, both of them can not encounter the needs of current scenario. To tackle this issue, this article proposed an image encryption algorithm based on Lorenz chaotic system and primitive irreducible polynomial substitution box. First, we have proposed 16 different S-boxes based on projective general linear group and 16 primitive irreducible polynomials of Galois field of order 256, and then utilized these S-boxes with combination of chaotic map in image encryption scheme. Three chaotic sequences can be produced by the disturbed of Lorenz chaotic system corresponding to variables x, y and z. We have constructed a new pseudo random chaotic sequence k_i based on x, y and z. The plain image is encrypted by the use of chaotic sequence k_i and XOR operation to get a ciphered image. To show the strength of presented image encryption, some renowned analyses are performed.

The Advanced Encryption Standard (AES) is widely used in different kinds of security applications. The substitution box (S-box) is the main component of many modern symmetric encryption ciphers that provides confusion between the secret key and ciphertext. The S-box component that is used in AES is fixed. If we construct this component dynamically, the encryption strength of AES would be greater than before. In this manuscript, we used chaotic logistic map, Mobius transformation and symmetric group $S_{256}$ to construct S-box for AES. The idea behind the proposed work is to make supplementary safe S-box. The presented S-box is analyzed for the following analyses: linear approximation probability (LP), nonlinearity (NL), differential approximation probability (DP), strict avalanche criterion (SAC), and bit independence criterion (BIC). The analyses show that the proposed technique is useful in generating high resistance S-box to known attacks.